Inspecting a slab of material

ABSTRACT

A system for inspecting a slab of material may include an optical fiber, a broadband light source configured to emit light having wavelengths of 780-1800 nanometers over the optical fiber, a beam-forming assembly configured to receive the light over the optical fiber and direct the light toward a slab of material, the beam-forming assembly may be configured to maintain the position of one or more elements within the beam-forming assembly despite changes in environmental temperature; a computer-controlled etalon filter configured to receive the light over the optical fiber, filter the light, and direct the light over the optical fiber; and a computer-controlled spectrometer configured to receive the light over the optical fiber after the light has been filtered by the etalon filter and after the light has been reflected from or transmitted through the slab of material and spectrally analyze the light.

CROSS REFERENCE TO OTHER APPLICATION

This application is a continuation-in-part with respect to U.S. patentapplication Ser. No. 16/048,712 filed on Jul. 30, 2018 which is acontinuation with respect to U.S. patent application Ser. No. 15/919,003filed on Mar. 12, 2018, which is a continuation-in-part with respect toU.S. patent application Ser. No. 15/410,328 filed on Jan. 19, 2017.

FIELD

The embodiments discussed in this disclosure are related to systems andmethods for inspecting a slab of material.

BACKGROUND

Thin slabs of material are often inspected to determine thickness usingknown methods of observation and analysis of Fabry Perot interferencefringes. In the case of a simple single slab of material, these knownmethods of inspection are based on the observation of interferencefringes in an etalon formed by the parallel interfaces of the sample.

Some of the commonly measured slabs of anisotropic materials such assapphire are bi-refringent in nature and used as wafer-carriers.Birefringence of the substrate implies that speed with which lightpropagates through such slab depends on polarization state of the light.Sapphire-plates are commonly used as wafer carriers for GaAs (GalliumArsenide) based wafers. Accordingly, an accurate determination ofthickness of the sapphire plates may be required while measuringthickness of GaAs patterned wafers residing on the sapphire-carrier.

However, employment of conventional methods of determining the thicknessof the slab of material may be substantially inaccurate with respect tothe aforesaid anisotropic materials at least at least due tobirefringence. Reasons for such inaccuracy in some instances may bebased on the thickness of the slab of anisotropic material being greaterthan about 50 μm, measurement noise resulting from Schott noise, thermalnoise, or the presence of stray light, or some combination thereof.Overall, the conventional methods for inspecting slab of material maynot only have limited spectral-resolution, but may also not be effectivewhen the slab of material to be measured exhibits birefringence and hasthe thickness as greater than 50 μm.

The subject matter claimed in this disclosure is not limited toembodiments that solve any disadvantages or that operate only inenvironments such as those described above. Rather, this background isonly provided to illustrate one example technology area where someembodiments described in this disclosure may be practiced.

SUMMARY

According to an aspect of one or more embodiments, a system forinspecting a slab of material may include single mode optical fiber. Thesystem may also include a broadband light source configured to emitlight in a range from 780 nanometers (nm) to 1800 nm over the opticalfiber. The system may also include a beam-forming assembly configured toreceive the light over the optical fiber and direct the light toward aslab of material. The system may also include a computer-controlledetalon filter configured to receive the light over the optical fibereither before the light is directed toward the slab of material or afterthe light has been reflected from or transmitted through the slab ofmaterial, filter the light, and direct the light over the optical fiber.The system may also include a computer-controlled spectrometerconfigured to receive the light over the optical fiber after the lighthas been filtered by the etalon filter and after the light has beenreflected from or transmitted through the slab of material andspectrally analyze the light.

According to an aspect of one or more embodiments, a system forinspecting a slab of material may include single mode optical fiber. Thesystem may also include a broadband light source configured to emitlight over the optical fiber and a beam-forming assembly. Thebeam-forming assembly may be configured to receive the light over theoptical fiber. The beam-forming assembly may also be configured to splitthe light, at a beam splitter, into first and second portions afterreceiving the light over the optical fiber. The beam-forming assemblymay also be configured to direct the first portion of the light towardthe slab of material. The beam-forming assembly may also be configuredto direct the second portion of the light onto a reflector that ismaintained at a substantially constant distance from the beam splitter.The beam-forming assembly may also be configured to combine the firstportion of the light after being reflected from the slab of material andthe second portion of the light after being reflected from thereflector. The beam-forming assembly may also be configured to directthe combined light over the optical fiber. The system may also include acomputer-controlled etalon filter configured to receive the light overthe optical fiber either before the light is directed toward the slab ofmaterial or after the light has been reflected from or transmittedthrough the slab of material, filter the light, and direct the lightover the optical fiber. The system may also include acomputer-controlled spectrometer configured to receive the light overthe optical fiber after the light has been filtered by the etalon filterand after the light has been reflected from or transmitted through theslab of material and spectrally analyze the light.

The objects and advantages of the embodiments will be realized andachieved at least by the elements, features, and combinationsparticularly pointed out in the claims. It is to be understood that boththe foregoing general description and the following detailed descriptionare exemplary and explanatory and are not restrictive of the invention,as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments will be described and explained with additionalspecificity and detail through the use of the accompanying drawings inwhich:

FIG. 1A illustrates a first example system for inspecting a slab ofmaterial;

FIG. 1B illustrates an example semiconductor-wafer (e.g. GaAs) mountedon a wafer-carrier or substrate (e.g. sapphire plate);

FIG. 2 illustrates a second example system for inspecting a slab ofmaterial;

FIG. 3 illustrates a third example system for inspecting a slab ofmaterial;

FIG. 4 illustrates a fourth example system for inspecting a slab ofmaterial;

FIG. 5A illustrates an example beam-forming assembly that may beemployed in the systems of FIGS. 1-4;

FIG. 5B illustrates an example beam-forming assembly that may beemployed in the systems of FIGS. 1-4;

FIG. 6A illustrates an example etalon filter that may be employed in thesystems of FIGS. 1, 3, and 4;

FIG. 6B illustrates an etalon operating at a Brewster-angle in FIG. 6A;

FIG. 7A illustrates an example etalon filter that may be employed in thesystem of FIG. 2;

FIG. 7B illustrates an example etalon filter operating at aBrewster-angle in FIG. 7A;

FIG. 8 illustrates a simulated spectrum that may be obtained using anyof the example systems of FIGS. 1-4;

FIG. 9A illustrates a simulated spectrum that may be measured by aspectrometer of any of the example systems of FIGS. 1-4;

FIG. 9B illustrates a simulated spectrum that may be reflected from aslab of material;

FIG. 9C illustrates a simulated normalized spectrum that may result fromdividing the simulated spectrum of FIG. 9B using the simulated spectrumof FIG. 9A; and

FIG. 10 is a flowchart of an example method for inspecting a slab ofmaterial.

DESCRIPTION OF EMBODIMENTS

According to at least one embodiment described in this disclosure, asystem for inspecting a slab of material may be configured to determinea topography of one or more surfaces of the slab of material and/ordetermine a thickness of the slab of material. The material of the slabof material may be, for example, a semiconductor device such as anycircuit, chip, or device that is fabricated on a silicon (Si) substratewafer, a MEMS structure, or an interconnect feature used in 3Dpackaging. In some embodiments, the material of the slab material may becarriers for GaAs (gallium arsenide) wafers such as Sapphire plates thatare anisotropic materials and that exhibit birefringence.

The system may include single mode optical fiber, a broadband lightsource, a beam-forming assembly, a computer-controlled etalon filter,and a computer-controlled spectrometer. The system may be employed todetermine the thickness of a slab of material using only a singleetalon, even when the thickness of the slab of material is greater thanabout 50 μm, resulting in a system having greater spectral resolutionthan known systems.

In these or other embodiments, the system may include a single modepolarization maintaining optical-fiber, a linearly polarized broadbandlight source, a beam-forming assembly, a polarization-rotator, acomputer-controlled etalon filter, and a computer-controlledspectrometer. Either the etalon within the etalon filter or dispersiveelement within the spectrometer, or both, may be oriented at apre-determined angle (e.g. Brewster angle) with respect to theincident-light or the polarized light received over the optical fiber.The system may be employed to determine the thickness of the slab of theanisotropic material exhibiting birefringence using only asingle-etalon, even when the thickness of the slab is greater than about50 μm, resulting in a system having greater spectral resolution thanknown systems and thereby a precise-determination of the thickness ofthe slab of the anisotropic material.

Embodiments of the present disclosure will be explained with referenceto the accompanying drawings.

FIG. 1A illustrates a first example system 100 for inspecting a slab ofmaterial 102, arranged in accordance with at least some embodimentsdescribed in this disclosure. Some of the commonly-measured slabs ofmaterials such as sapphire-plates exhibit birefringence. Sapphire-platesare commonly used as wafer-carriers during processing of wafer ofsemiconductor-materials such as Gallium-Arsenide (GaAs) based wafers. Insome embodiments, the system 100 may be configured to determinethickness of slabs of wafer-carriers exhibiting birefringence. As may beunderstood, birefringence of the substrate implies that speed with whichlight propagates through the slab depends on a polarization state of thelight. For example, FIG. 1B illustrates an example semiconductor waferof Gallium-Arsenide (GaAs) that may be supported on an examplewafer-carrier such as a Sapphire Plate.

In general, the system 100 may be configured to inspect the slab ofmaterial 102 (which may include a slab of wafer-carriers such assapphire-plates in some embodiments) in order to determine a topographyof a front surface 104 and/or a back surface 105 of the slab of material102 and/or in order to determine a thickness 106 of the slab of material102. To perform the inspection, the system 100 may include single modeoptical fibers 108, 110, 112, and 114 (which may be polarizationmaintaining in some embodiments), a broadband light source 116 (whichmay be linearly polarized in some embodiments), a beam-forming assembly118, a directional element 126, a half-wave plate 119 acting as apolarization-rotator, an etalon-filter 120, and a spectrometer 122,wherein both the etalon-filter 120 and the spectrometer 122 arecontrolled by a computer 124.

The broadband light-source 116 may be configured to emit light over theoptical-fiber 108. In some embodiments, the linearly polarized broadbandlight-source 116 may be configured to emit a linearly polarized light orplane-polarized light over the optical-fiber 108, such that a plane ofpolarization, i.e. the direction of polarization is pre-defined. Thedirectional element 126 (e.g. an optical circulator) may be configuredto receive the light from the broadband-light source 116 over theoptical fiber 108 and direct the light to the beam forming assembly 118over the optical fiber 110. In some embodiments, the light directed overthe optical fiber 110 may be plane-polarized and the optical fiber 110may be configured to maintain the polarization, such as indicated above.

In one the embodiment the broadband light source 116 may emit light inthe wavelength range between 1100 nanometers (nm) and 1800 nm. Thebroadband light source may be implemented as a Superluminescent LightEmitter Device (SLED), such as Thorlabs part number SLD1325. The opticalcomponents including the optical fiber 108, the circulator 126, theoptical fiber 110, the beam forming assembly 118, the optical fiber 112,the half wave plate 119, the etalon filter 120, the optical fiber 114,and the spectrometer 122 may be configured to operate in the samewavelength range as the light emitted by the broadband light source 116.The SLED may provide the advantage that emitted radiation can propagatewithout significant attenuation through Si and GaAs and may be used toprobe layers of the semiconductor structures obscured by layer of Si,GaAs or similar material. Furthermore this according to Center forDevice Radiological Health (CDRH) regulation, SLED is eye-safe as longas user-accessible light power does not exceed 1 milliwatt (mW).

In another embodiment, the broadband light source 116 may emit light inwavelength range of 780-1000 nm. The broadband light source 116 may beimplemented as a SLED such as Thorlabs model SLD880S-A7. A broadbandlight source 116 that emits light in the wavelength range of 780-1000 nmmay allow use of a spectrometer employing silicon-based detectors, whichmay be relatively inexpensive. Additionally or alternatively, IndiumGallium Arsenide (InGaAs) detectors may be used, such as, for example,in a system including a broadband light source that emits light innear-infrared wavelengths. The silicon-based detectors can be cooled ornot cooled depending on desired signal-to-noise ratio for the entiresystem. In some embodiments silicon-based detectors operating in systemsusing visible light may be less noisy than infrared detectors havingsimilar size and operating temperature.

The beam-forming assembly 118 may be configured to receive the lightover the optical fiber 110 and direct the light toward the slab ofmaterial 102 in which the half-wave plate 119 may be omitted.Additionally or alternatively, the beam-assembly 118 may be configuredto receive the light over the optical fiber 110 and direct the lighttowards the slab of material 102 via the half-wave plate 119 or anyother known polarization rotator as known in the art. The half-waveplate 119 controls plane of polarization of light impinging the slab ofmaterial 102 by rotating the plane of polarization through a pre-definedangle. Overall, a pre-defined plane or direction of polarization asrendered by the linearly polarized broadband light source 116 as well asthe controlled rotation of the plane of polarization as rendered by thehalf-wave plate 119 facilitates a constant polarization of the lightwithin the slab of material 102.

The beam-assembly 118 may be further configured to receive the lightreflected from the slab of material 102 and direct the light back to thedirectional element 126 over the optical fiber 110. The etalon filter120, as controlled by the computer 124, may be configured to receive thelight over the optical fiber 112 after the light has been reflected fromthe slab of material 102, filter the light, and direct the light overthe optical fiber 114. The spectrometer 122, as controlled by thecomputer 124, may be configured to receive the light over the opticalfiber 114, after the light has been filtered by the etalon filter 120and after the light has been reflected from the slab of material 102,and spectrally analyze the light. The spectral analysis of the light mayinclude determining a topography of the front surface 104 and/or theback surface 105 of the slab of material 102 and/or determining thethickness 106 of the slab of material 102.

In a some embodiments (e.g., instances in which the light is polarized),an etalon 604 or 704 (see FIG. 6 and FIG. 7) may be placed within theetalon filter 120 at a ‘Brewster angle’ with respect to the incidentpolarized light (as illustrated in FIG. 6B and FIG. 7B) in order toreduce or eliminate reflection of the polarized light from thefront-surface of the etalon. In addition, in case the spectrometer 122comprises grating as a dispersive element, then the efficiency of thegrating may be improved or optimized by maintaining a specific-anglebetween grooves of the grating and the plane of polarization of thelight incident upon the grating. In embodiments in which thespectrometer 122 includes a prism as the dispersive element, then theprism may be oriented with respect to the incident polarized light in amanner such that the light impinges the prism at the Brewster angle,thereby reducing or eliminating reflection loss on a first surface ofthe prism of the spectrometer.

The computer 124 may be electrically coupled to the etalon filter 120and to spectrometer 122. In these and other embodiments, the computer124 may be configured to determine a topography of the front surface 104and/or the back surface 105 of the slab of material 102 and/or determinethe thickness 106 of the slab of material 102. The computer 124 mayinclude a processor and a memory. The processor may include, forexample, a microprocessor, microcontroller, digital signal processor(DSP), application-specific integrated circuit (ASIC), aField-Programmable Gate Array (FPGA), or any other digital or analogcircuitry configured to interpret and/or to execute program instructionsand/or to process data. In some embodiments, the processor may interpretand/or execute program instructions and/or process data stored in thememory. The processor may execute instructions to perform operationswith respect to the spectrometer 122 in order to determine a topographyof the front surface 104 and/or the back surface 105 of the slab ofmaterial 102 and/or determine the thickness 106 of the slab of material102. The memory may include any suitable computer-readable mediaconfigured to retain program instructions and/or data for a period oftime. By way of example, and not limitation, such computer-readablemedia may include tangible and/or non-transitory computer-readablestorage media including Random Access Memory (RAM), Read-Only Memory(ROM), Electrically Erasable Programmable Read-Only Memory (EEPROM),Compact Disc Read-Only Memory (CD-ROM) or other optical disk storage,magnetic disk storage or other magnetic storage devices, flash memorydevices (e.g., solid state memory devices), or any other storage mediumwhich may be used to carry or store desired program code in the form ofcomputer-executable instructions or data structures and which may beaccessed by a general-purpose or special-purpose computer. Combinationsof the above may also be included within the scope of computer-readablemedia. Computer-executable instructions may include, for example,instructions and data that cause a general-purpose computer,special-purpose computer, or special-purpose processing device toperform a certain function or group of functions.

The etalon filter 120 may be a fixed etalon filter or may be a tunableetalon filter. In principle, if the optical thickness of the etalonfilter 120 is known, and if the slab of material 102 is placed at aperfectly normal direction to the light from the beam-forming assembly118, the etalon filter 120 may be a fixed etalon filter and may not needcalibration. However, if any of these conditions are not met, the etalonfilter 120 may need to be a tunable etalon filter.

In one tunable embodiment, the etalon filter 120 may includemultiple-etalons with each etalon including two parallel reflectivesurfaces and with each etalon mounted in a computer-controlled motorizedwheel. In another tunable embodiment, the etalon filter 120 may includetwo parallel reflective surfaces with at least one of the two parallelreflective surfaces being mounted on a computer-controlled linear motionstage. In either of these tunable embodiments, the etalon filter 120 maybe tunable in order to allow the optical thickness of the etalon filterto be similar to the thickness 106 of the particular slab of material102 that is to be inspected by the system 100. For example, the etalonfilter 120 may include two parallel reflective surfaces separated by adistance, which is the optical thickness of the etalon filter 120, andduring calibration of the etalon filter 120 the distance may be adjustedso that the distance is within 250 microns of the thickness 106 of theslab of material 102.

This calibration may include placing a slab of material of a knownrefractive index n and known thickness tin the system 100 and measuringits apparent optical thickness of calibration standard (AOTCS). Theresult of the measurement is used to calculate a calibration factor CFgiven by CF=n*t/AOTCS. When measuring actual slabs of material, theoptical thickness (OT) of the slabs of material is given by OT=CF*AOT,where AOT is the measured apparent optical thickness.

The system 100 may be advantageously employed when the optical thickness(OT) of the etalon filter 120 is similar to the thickness of the slab ofmaterial 102 to be inspected, such as within 250 microns of the slab ofmaterial 102 to be inspected. The system 100 may also be employed wheninterference happens between the front surface 104 of the slab ofmaterial 102 and a reflector 508 (see FIG. 5), enabling a topography ofthe front surface 104 and/or the back surface 105 of the slab ofmaterial 102 to be determined.

In the case of a single parallel plate forming a simple non-absorbingetalon, the reflection of the light propagating through a slab ofmaterial is given by the Equation:

$\begin{matrix}{R = \frac{F\; {\sin \left( {\delta/2} \right)}^{2}}{1 + {F\; {\sin \left( {\delta/2} \right)}^{2}}}} & (1)\end{matrix}$

where the coefficient of finesse F is defined by the Equation:

$\begin{matrix}{F = \frac{4\; r}{\left( {1 - r} \right)^{2}}} & (2)\end{matrix}$

where r is a Fresnel reflection at the interfaces of the slab ofmaterial forming the etalon, and where the optical path difference δ isgiven by the Equation:

$\begin{matrix}{\delta = {\frac{2\; \pi}{\lambda}2{nd}}} & (3)\end{matrix}$

if one assumes that optical radiation having wavelength λ propagates inthe direction perpendicular to faces of the slab of material havingrefractive index n and thickness d. Since bandwidth of a light source isfinite in this instance, for the sake of simplicity we may ignorespectral dispersion of the slab of material 102 and we may assume thatthe refractive index does not depend on the wavelength.

For a non-absorbing etalon, the law of conservation energy requires thefollowing Equation:

T+R=1  (4)

And therefore, directly from Equations (1) and (3) above, we may derivethe following Equation:

$\begin{matrix}{T = \frac{1}{1 + {F\; {\sin \left( {\delta/2} \right)}^{2}}}} & (5)\end{matrix}$

The reflection and transmission given by Equations (1) and (5) revealoscillations known as Fabry-Perot fringes. Directly from Equations (1)and (2) we see that spacing between fringes on such an etalon in theabsence of the spectral dispersion (and sometimes referred to as freespectral range) is given by the Equation:

$\begin{matrix}{{\Delta \; \lambda_{FSR}} = \frac{\lambda^{2}}{2\; {nd}}} & (6)\end{matrix}$

Or in frequency domain spacing between fringes is constant and equal tothe Equation:

$\begin{matrix}{{\Delta \; \upsilon_{FSR}} = \frac{c}{2{nd}}} & (7)\end{matrix}$

The intensity of the light reflected from the sample I(λ) is givensimply by product of the intensity of light emitted from a broadbandlight source (e.g., a linearly polarized broadband light source in someinstances) I_(source)(λ) and reflection of the sample R(λ) given byEquation (1), according to the following Equation:

I(λ)=R(λ)·I _(source)(λ)  (8)

Since the spectrum of the source may be measured independently, themeasurement of the spectrum of reflected beam can be used to findreflection of the sample, according to the Equation:

$\begin{matrix}{{R(\lambda)} = \frac{I(\lambda)}{I_{source}(\lambda)}} & (9)\end{matrix}$

When the reflection function is established from Equation (1), one canuse the measurement of spacing between fringes or the frequency ofobserved fringes to establish the thickness of the slab of materialaccording to the following Equation:

$\begin{matrix}{F = \frac{4\; r}{\left( {1 - r} \right)^{2}}} & (10)\end{matrix}$

The observed spectrum by spectrograph comprising a spectrometer andarray detector are given by convolution of intensity spectrum impingingan entrance slit I(λ) of the spectrometer and a response function of thespectrometer

(λ,{tilde over (λ)}) according to the Equation:

I _(observed)(λ)=∫₀ ^(∞)

(λ,{tilde over (λ)})*I({tilde over (λ)})d{tilde over (λ)}  (11)

The response function of the spectrometer can be modelled by a simpleboxcar function:

$\begin{matrix}{{\left( {\lambda,\overset{\sim}{\lambda}} \right)} = \frac{\theta \left( {{\Delta \; {\lambda/2}} - {{\lambda - \lambda^{\sim}}}} \right)}{\Delta \; \lambda}} & (12)\end{matrix}$

where θ is a Heaviside step function, Δλ is bandwidth of spectrograph, λis a wavelength measured by spectrograph, and {tilde over (λ)} iswavelength of incoming radiation.

In this simplified model we have neglected additional broadening causedby finite pixel size, and aberration of the spectrometer.

In the case of the system 100 being employed when the optical thicknessof the etalon filter 120 is similar to the thickness of the slab ofmaterial 102 to be inspected, the transmission of the reference may begiven by the following Equation:

$\begin{matrix}{T_{ref} = \frac{1}{1 + {F_{ref}{\sin \left( {\delta_{ref}/2} \right)}^{2}}}} & (13)\end{matrix}$

where finesse coefficient and optical path difference are defined justas in the case of our sample by the following Equations:

$\begin{matrix}{{F_{ref} = \frac{4\; r_{ref}}{\left( {1 - r_{ref}} \right)^{2}}}{and}} & (14) \\{\delta_{ref} = {\frac{2\; \pi}{\lambda}n_{ref}d_{ref}}} & (15)\end{matrix}$

The intensity of light emitted by the broadband light source 116,reflected by the slab of material 102, and impinging a slit of thespectrometer 122, is given by:

I(λ)=T _(ref)(λ)·R(λ)·I _(source)(λ)  (16)

or in frequency domain

I(k)=T _(ref)(k)·R(k)·I _(source)(k)  (17)

where k=1/λ and

I _(observed)(k)=∫₀ ^(∞)

(k,{tilde over (k)})*I({tilde over (k)})d{tilde over (k)}  (18)

Since both R(L) and T_(ref) (λ) functions reveal narrow fringes of asimilar period (since the reference etalon optical path difference (OPD)has been selected to be close to the sample OPD), their product willreveal oscillations corresponding to beats of the fringes in the sampleand the reference etalon.

Origin of the observed beats can be understood using Fourier expansionof the R (k), and T_(ref) (k), according to the following Equation:

$\begin{matrix}{{R(k)} = {a_{0} + {\sum\limits_{n = 1}^{\infty}\left( {{a_{n}\cos \; \frac{n\; \pi \; k}{{\Delta\upsilon}_{FSR}}} + {b_{n}\sin \; \frac{n\; \pi \; k}{{\Delta\upsilon}_{FSR}}}} \right)}}} & (19)\end{matrix}$

where a₀, a_(n), and b_(n) are constants. Since R(k) is an even functionwe have b_(n·)=0 for all n. So R(k) is given by the Equation:

$\begin{matrix}{{R(k)} = {a_{0} + {\sum\limits_{n = 1}^{\infty}{a_{n}\cos \; \frac{n\; \pi \; k}{\Delta \; \upsilon_{FSR}}}}}} & (20)\end{matrix}$

Similar argument for the T_(ref) (k) leads to the following Equation:

$\begin{matrix}{{{T_{ref}(k)} = {a_{{ref},0} + {\sum\limits_{n = 1}^{\infty}{a_{{ref},n}\cos \; \frac{n\; \pi \; k}{{\Delta\upsilon}_{{ref},{FSR}}}}}}}{where}} & (21) \\{{\Delta \; \upsilon_{FSR}} = \frac{c}{2\; n_{ref}d_{ref}}} & (22)\end{matrix}$

where n_(ref) is refractive index of the reference etalon, and d_(ref)is the thickness of the etalon.

Therefore, the product may be found in the following Equation:

$\begin{matrix}{{{R(k)} \cdot {T_{ref}(k)}} = {\left( {a_{0} + {\sum\limits_{n = 1}^{\infty}{a_{n}\cos \; \frac{n\; \pi \; k}{\Delta \; v_{FSR}}}}} \right)\left( {a_{{ref},0} + {\sum\limits_{m = 1}^{\infty}{a_{{ref},m}\cos \; \frac{m\; \pi \; k}{{\Delta\upsilon}_{{ref},{FSR}}}}}} \right)}} & (23)\end{matrix}$

By unfolding brackets, we get the following Equation:

$\begin{matrix}{{{R(k)} \cdot {T_{ref}(k)}} = {{a_{0}a_{{ref},\; 0}} + {a_{0}a_{{ref},1}\cos \; \frac{1\pi \; k}{\Delta \; \upsilon_{{ref},{FSR}}}} + {a_{1}a_{{ref},0}\cos \; \frac{1\pi \; k}{\Delta \; \upsilon_{FSR}}} + {a_{1}a_{{ref},1}\cos \; \frac{1\; \pi \; k}{\Delta \; \upsilon_{FSR}}\cos \; \frac{1\pi \; k}{\Delta \; \upsilon_{{ref},{FSR}}}} + \ldots}} & (24)\end{matrix}$

Then from the above we get the following Equation:

$\begin{matrix}{{{R(k)} \cdot {T_{ref}(k)}} = {{a_{0}a_{{ref},\; 0}} + {a_{0}a_{{ref},1}\cos \; \frac{1\pi \; k}{\Delta \; \upsilon_{{ref},{FSR}}}} + {a_{1}a_{{ref},0}\cos \; \frac{1\pi \; k}{\Delta \; \upsilon_{FSR}}} + {a_{1}a_{{ref},1}\cos \; \frac{1\; \pi \; k}{\Delta \; \upsilon_{FSR}}\cos \; \frac{1\pi \; k}{\Delta \; \upsilon_{{ref},{FSR}}}} + \ldots}} & (25)\end{matrix}$

Since the thicknesses of the reference etalon and the sample aresimilar, we can use the trigonometric Equation:

$\begin{matrix}{{{R(k)} \cdot {T_{ref}(k)}} = {{a_{0}a_{{ref},\; 0}} + {a_{0}a_{{ref},1}\cos \; \frac{1\pi \; k}{\Delta \; \upsilon_{{ref},{FSR}}}} + {a_{1}a_{{ref},0}\cos \; \frac{1\pi \; k}{\Delta \; \upsilon_{FSR}}} + {\frac{1}{2}a_{1}a_{{ref},1}\cos \; \left( {\frac{1\pi \; k}{\Delta \; \upsilon_{ref}} - \frac{1\pi \; k}{\Delta \; \upsilon_{{ref},{FSR}}}} \right)} + {\frac{1}{2}a_{1}a_{{ref},1}\cos \; \left( {\frac{1\; \pi \; k}{\Delta \; \upsilon_{ref}} + \; \frac{1\pi \; k}{\Delta \; \upsilon_{{ref},{FSR}}}} \right)} + \ldots}} & (26)\end{matrix}$

By substituting Equations (7) and (22) and rearranging terms, we get theEquation:

$\begin{matrix}{{{R(k)} \cdot {T_{ref}(k)}} = {{a_{0}a_{{ref},0}} + {\frac{1}{2}a_{1}a_{{ref},1}{\cos \left( \frac{2\; {\pi \left( {{n_{ref}d_{ref}} - {nd}} \right)}k}{c} \right)}} + {\frac{1}{2}a_{1}a_{{ref},1}{\cos \left( \frac{2\; {\pi \left( {{n_{ref}d_{ref}} + {nd}} \right)}k}{c} \right)}} + {a_{0}a_{{ref},1}\cos \; \frac{1\pi \; k}{{\Delta\upsilon}_{{ref},{FSR}}}} + {a_{1}a_{{ref},0}\cos \; \frac{1\pi \; k}{\Delta \; \upsilon_{FSR}}} + \ldots}} & (27)\end{matrix}$

The first and the second terms are slow varying terms in comparison toΔν_(FSR). Therefore, we can rewrite the above Equation as the Equation:

$\begin{matrix}{{{R(k)} \cdot {T_{ref}(k)}} = {{a_{0}a_{{ref},0}} + {\frac{1}{2}a_{1}a_{{ref},1}{\cos \left( \frac{2\; {\pi \left( {{n_{ref}d_{ref}} - {nd}} \right)}k}{c} \right)}} + {{rapidly}\mspace{14mu} {varying}\mspace{14mu} {terms}\mspace{14mu} {in}\mspace{14mu} k}}} & (28)\end{matrix}$

Since the spectrograph response function is filtering out the rapidlyvarying terms, the observed signal has a form of the Equation:

I _(observed)(k)=∫0∞

(k,{tilde over (k)})·R({tilde over (k)})·T _(ref)({tilde over (k)})·I_(source)({tilde over (k)})d _(k)  (29)

Since the light source is broadband and has a slowly varying spectrum infunction of k, we have the following Equations:

$\begin{matrix}{{I_{observed}(k)} = {{I_{source}(k)}{\int_{0}^{\infty}{{{\left( {k,\overset{\sim}{k}} \right)} \cdot {R\left( \overset{\sim}{k} \right)} \cdot {T_{ref}\left( \overset{\sim}{k} \right)}}d\; \overset{\sim}{k}}}}} & (30) \\{{I_{observed}(k)} = {{I_{source}(k)}{\int_{0}^{\infty}{{{\left( {k,\overset{\sim}{k}} \right)} \cdot \left\lbrack {{a_{0}a_{{ref},0}} + {\frac{1}{2}a_{1}a_{{ref},1}{\cos \left( \frac{2\; {\pi \left( {{n_{ref}d_{ref}} - {nd}} \right)}\overset{\sim}{k}}{c} \right)}} + {{rapidly}\mspace{14mu} {varying}\mspace{14mu} {terms}\mspace{14mu} {in}\mspace{14mu} \overset{\sim}{k}}} \right\rbrack}d\; \overset{\sim}{k}}}}} & (31)\end{matrix}$

Since the spectrograph response function does not affect slowly varyingfunctions (because it acts as a smoothing filter), we get from above theEquation:

$\begin{matrix}{\frac{I_{observed}(k)}{I_{source}(k)} = {{a_{0}a_{{ref},0}} + {\frac{1}{2}a_{1}a_{{ref},1}{\cos \left( \frac{2\; {\pi \left( {{n_{ref}d_{ref}} - {nd}} \right)}k}{c} \right)}} + {{rapidly}\mspace{14mu} {varying}\mspace{14mu} {terms}\mspace{14mu} {in}\mspace{14mu} k}}} & (32)\end{matrix}$

The above equation can be used directly to measure the thickness of arelatively thick slab of material using the system 100 which employs thereference etalon filter 120. The system 100 may accomplish thismeasurement by measuring the spectrum of the broadband light source 116,measuring the spectrum of the light reflected from the slab of material102, and transmitted through the reference etalon filter 120,calculating ratio

$\frac{I_{observed}(k)}{I_{source}(k)},$

and finding experimentally the lowest non-zero angular frequency of theobserved oscillations in function of k, according to the followingEquation:

$\begin{matrix}{\Omega = \frac{2\; \pi \; {\left( {{n_{ref}d_{ref}} - {nd}} \right)}}{c}} & (33)\end{matrix}$

Note that Ω may have a unit of time, since it is the frequency of thefringes observed in the frequency space.

If it is known that (n_(ref)d_(ref)−nd)>0, then the thickness of theslab of material 102 can be found directly from the Equation:

$\begin{matrix}{d = {\frac{2\; {\pi \left( {n_{ref}d_{ref}} \right)}}{n} - {\Omega \; c}}} & (34)\end{matrix}$

The value of Ω from measured ratio

$\frac{I_{observed}(k)}{I_{source}(k)}$

can be found using standard numerical techniques including but notlimited to techniques based on Fourier transforms.

If it is known that (n_(ref)d_(ref)−nd)≤0 then the thickness of thelayer can be found directly from the Equation:

$\begin{matrix}{d = {{\Omega \; c} - \frac{2\; {\pi \left( {n_{ref}d_{ref}} \right)}}{n}}} & (35)\end{matrix}$

Any ambiguity resulting from the choice between Equations (34) and (35)can be facilitated by use of a plurality of reference etalons havingdifferent optical thicknesses n_(ref)d_(ref) or by use of the samereference etalon at normal and at a tilted angle which would increasethe optical path in the reference etalon.

If the approximate thickness of the measured slab is known, then oneetalon may be employed having a known and slightly larger thickness thanthe thickness of the slab of material 102 to measure the exact thickness106 of the slab of material 102 using the system 100. For example, inthis situation, the system 100 may be employed to measure the thickness106 of the slab of material 102 by the following procedure:

1. Measuring the reference spectrum (as shown in FIG. 9A) of thebroadband light source 116 by placing a mirror in place of the slab ofmaterial 102 using the system 100 in which the etalon filter 120 istemporarily removed, or in which the slab of material 102 is replaced bya very thick etalon filter having an optical thickness much greater thanthe optical thickness 106 of the measured slab of material 102.2. Measuring the signal spectrum (as shown in FIG. 9B) of the lightreflected from the slab of material 102 having a known refractive indexn, and passing through the etalon filter 120 having a known thicknesswhich is known to be slightly larger than the thickness 106 of themeasured slab of material 102.3. Calculating a normalized spectrum (as shown in FIG. 9C) by dividingthe signal spectrum by the reference spectrum.4. Calculating the frequency Ω of observed oscillations in thenormalized spectrum.5. Calculating the thickness 106 of the slab of material 102 usingEquation 34.

The frequency calculation using a normalized signal in step 3 in theabove procedure can be performed using one of many standard methods ofsignal processing including, but not limited to, Fourier transformmethods, fitting oscillating model function methods, and investigatingposition of the maxima and minima of the oscillations shown in FIG. 9C.

Similarly, if the approximate thickness of the measured slab of material102 is known, then one etalon having a known and slightly smallerthickness than the thickness 106 of the slab of material 102 may beemployed to measure the exact thickness 106 of the slab of material 102using system 100. For example, in this situation, the system 100 may beemployed to measure the thickness 106 of the slab of material 102 by thefollowing procedure:

1. Measuring the reference spectrum (as shown in FIG. 9A) of thebroadband light source 116 by placing a mirror in place of the slab ofmaterial 102 using the system 100 in which the etalon filter 120 istemporarily removed, or in which the slab of material 102 is replaced bya very thick etalon filter having an optical thickness much greater thanthe optical thickness 106 of the measured slab of material 102.2. Measuring the signal spectrum (as shown in FIG. 9B) of the lightreflected from the slab of material 102 having a known refractive indexn, and passing through the etalon filter 120 having a known thicknesswhich is known to be slightly smaller than the thickness 106 of themeasured slab of material 102.3. Calculating a normalized spectrum by dividing the signal spectrum bythe reference spectrum as shown in FIG. 13C.4. Calculating the frequency Ω of observed oscillations in thenormalized spectrum.5. Calculating the thickness 106 of the slab of material 102 usingEquation 35.

Measurements using N etalons having different optical thicknesses may beperformed using the following steps, where N=2, 3, . . . :

1. Measuring the reference spectrum (as shown in FIG. 9A) of thebroadband light source 116 by placing a mirror in place of the slab ofmaterial 102 using the system 100 in which the etalon filter 120 istemporarily removed, or in which the slab of material 102 is replaced byvery thick etalon filter of having an optical thickness much greaterthan the optical thickness 106 of the measured slab of material 102.2. Measuring the signal spectra (as shown in FIG. 9B) of the lightreflected from the slab of material 102 having a known refractive indexn, and passing through each of the employed etalons i=1, 2.3. Calculating a normalized spectra (as shown in FIG. 9C) by dividingthe signal spectra by the reference spectrum.4. Calculating the frequency f of observed oscillations in thenormalized spectrum.

Finding an approximate solution d of the (overdetermined) system ofequations following from Equation (33) using the following Equation:

$\begin{matrix}{\Omega_{i} = \frac{2\; \pi {\left( {{n_{{ref},i}d_{{ref},i}} - {nd}} \right)}}{c}} & (36)\end{matrix}$

where i=1, . . . , N, and n_(ref,i) is a refractive index of etalonhaving index I and d_(ref,i) is the thickness of the etalon having anindex i.

FIG. 2 illustrates a second example system 200 for inspecting a slab ofmaterial, arranged in accordance with at least some embodimentsdescribed in this disclosure. Since the system 200 is similar in manyrespects to the system 100 of FIG. 1, only the differences between thesystem 200 and the system 100 will be discussed herein.

In additional to elements in common with the system 100, the system 200may include a second directional element 213, an etalon filter 220, anda single mode optical fiber 215, which may be a polarization maintainingoptical fiber in some embodiments.

The second directional element 213 may be configured to receive thelight from the directional element 126 over the optical fiber 112 anddirect the light to the etalon filter 220 over the optical fiber 215.The etalon filter 220 may be configured similarly to the etalon filter120 of FIG. 1, except that the etalon filter 220 may be configured toreceive the light from the second directional element 213 over theoptical fiber 215 after the light has been reflected from the slab ofmaterial 102 and direct the light back to the second directional element213 over the optical fiber 215. The spectrometer 122 of the system 200may then be configured to receive the light from the second directionalelement 213 over the optical fiber 114.

FIG. 3 illustrates a third example system 300 for inspecting a slab ofmaterial, arranged in accordance with at least some embodimentsdescribed in this disclosure. Since the system 300 is similar in manyrespects to the system 100 of FIG. 1, only the differences between thesystem 300 and the system 100 be discussed herein.

In additional to elements in common with the system 100, the system 300may include a single mode optical fiber 317 (which may be a polarizationmaintaining optical fiber in some embodiments) and an etalon filter 320.

The etalon filter 320 may be configured similarly to the etalon filter120 of FIG. 1, except that the etalon filter 320 may be configured toreceive the light (which may be linearly polarized in some embodiment)from the broadband light source 116 over the optical fiber 317 beforethe light is directed toward the slab of material 102 and then, afterfiltering the light, direct the light over the optical fiber 108 to thedirectional element 126. Then, after the light has been reflected fromthe slab of material 102, the spectrometer 122 may be configured toreceive the light from the directional element 126 over the opticalfiber 112.

FIG. 4 illustrates a fourth example system 400 for inspecting a slab ofmaterial, arranged in accordance with at least some embodimentsdescribed in this disclosure. Since the system 400 is similar in manyrespects to the system 100 of FIG. 1, only the differences between thesystem 400 and the system 100 be discussed herein.

In additional to elements in common with the system 100, the system 400may include a first beam-forming assembly 418 a and a secondbeam-forming assembly 418 b.

The beam-forming assembly 418 a may be similar to the beam-formingassembly 118 of FIG. 1 except that the beam-forming assembly is notconfigured to receive the light reflected back from the slab of material102. Instead, the light directed from the beam-forming assembly 418 a istransmitted through the slab of material 102 toward the secondbeam-forming assembly 418 b via a first half wave plate 119 a (or anyother polarization rotator) the controls the plane of polarization ofthe light. The second beam-forming assembly 418 b may be configured toreceive the light transmitted through the slab of material 102 via asecond half wave plate 119 b (or any other polarization rotator), anddirect the light to the etalon-filter 120 over the optical fiber 112.The etalon filter 120 may then be configured to receive the light fromthe second beam-forming assembly 118 b over the optical fiber 112 afterthe light has been transmitted through the slab of material. In someembodiments, the system 400 may omit the half wave plates 119.

The systems 200, 300, and 400 of FIGS. 2, 3, and 4, respectively, mayoperate according to very similar principles. For example, since allcomponents of the optical systems may be linear in light intensity, theordering of the reference etalon (the etalon filter) and the sample (theslab of material) does not affect the signal produced by the system.Therefore, the systems 200 and 300 may produce substantially the samesignal. The main difference between the systems 200 and 300 is use of areference etalon operating in the transitive mode and the reflectivemode, respectively. A similar analysis may be performed using eithersystem, leading to Equations (34) and (35).

FIG. 5A illustrates an example beam-forming assembly 500, arranged inaccordance with at least some embodiments described in this disclosure.The beam-forming assembly 500 may be employed as the beam-formingassembly 118 in the system 100 of FIG. 1, in the system 200 of FIG. 2,and in the system 300 of FIG. 3. The beam-forming assembly 500 mayinclude lenses 502 and 504. The beam-forming assembly 500 may alsooptionally include a beam splitter 506 and a reflector 508. The lens 502may be configured to receiving the light over the optical fiber 110 andcollimate and direct the light toward the beam splitter 506. The beamsplitter 506 may be configured to split the light from the lens 502 intofirst and second portions, direct the first portion of the light towardthe lens 504, and direct the second portion of the light onto areflector 508. The lens 504 may be configured to receive the firstportion of the light from the beam splitter 506, direct the firstportion of the light toward the slab of material 102, and direct thefirst portion of the light after being reflected from the slab ofmaterial 102 back toward the beam splitter 506. Further, the reflector508 may be configured to receive the second portion of the light fromthe beam splitter 506 and reflect the second portion of the light backtoward the beam splitter 506. The beam splitter 506 may be furtherconfigured to combine the first portion of the light after beingreflected from the slab of material 102 and the second portion of thelight after being reflected from the reflector 508, and then direct thecombined light toward the lens 502. Finally, the lens 502 may beconfigured to receive the combined light and direct the combined lightover the optical fiber 110.

The reflector 508 may be implemented, among other ways, as a mirror, orcorner cube retro-reflector. It may be important to maintain awell-controlled distance between beam splitter 506 and reflector 508. Insome circumstances a change of temperature may result in change in thedistance between the beam splitter 506 and the reflector 508. To reducethe likelihood of a change in temperature from changing the distancebetween the beam splitter 506 and the reflector 508, in someembodiments, the entire beam-forming assembly 500 may be manufacturedfrom the materials having small coefficient of thermal expansion suchas, for example, Invar.

Additionally or alternatively, beam-forming assembly 500 may bemaintained at a constant temperature or close to a constant temperaturevia of a temperature controller 555. FIG. 5B illustrates an examplebeam-forming assembly 500, arranged in accordance with at least someembodiments described in this disclosure. The temperature controller 555may include a temperature sensor, a heater, and feedback electronicsconfigured to assure that temperature of the beam-forming assembly 500remains independent on the environment temperature. In some casestemperature controller 555 may also include a mechanism to providecooling, such as, for example, a thermoelectric cooler.

The beam-forming assembly 500 may be employed to gauge the optical pathdifference (OPD) between the first portion of the light and the secondportion of the light, which can be used to measure the distance betweenthe front surface 104 of the slab of material 102 and the lens 504.

The topography of the front surface 104 of the slab of material 102 maybe determined by placing a slab of material 102 on an XY motion stageperpendicular to the light beam impinging the front surface 104 of theslab of material 102, with the front surface 104 being parallel to themotion of the XY motion stage, and by collecting a data set comprisingthe data set on a large number M comprising the x_(j) and y_(j)coordinates of the point where the beam is impinging the front surface104 of the slab of material 102 and the distance between stationary lens504 and the front surface 104 of the slab of material 102 z_(j), wherej=1 . . . M. The set of points (x_(j), y_(j), z_(j)) can then be used toconstruct a three dimensional map of the front surface 104 of the slabof material 102. A similar procedure may be performed to determine thetopography of the back surface 105 of the slab of material 102.

As noted above, although the beam splitter 506 and the reflector 508 maybe beneficial in some embodiments of the beam-forming assembly 500, itis understood that in other embodiments the beam-forming assembly mayinstead omit the beam splitter 506 and the reflector 508. For example,the beam-forming assembly 500 may be employed as the beam-formingassembly 118 a and as the beam-forming assembly 118 b in the system 400of FIG. 4 and since the light only passes through the beam assemblies118 a and 118 b in a single direction in the system 400, the beamsplitter 506 and the reflector 508 may be omitted.

The beam directed towards the reflector 508 may be blocked by beamshutter 510 to avoid extra interference, such as in measurement modeswhere the usage of the reflector 508 is not required. The beam shutter510 may be operated manually or may be computer controlled.

FIG. 6A illustrates an example etalon filter 600, arranged in accordancewith at least some embodiments described in this disclosure. The etalonfilter 600 may be employed as the etalon filter 120 in the systems 100and 400 of FIGS. 1 and 4, respectively, and as the etalon filter 320 inthe system 300 of FIG. 3.

The etalon filter 600 may include a first beam collimator 602, an etalon604, and a second beam collimator 606. The first beam collimator 602 maybe connected to the optical fiber 112 and the second beam collimator 606may be connected to the optical fiber 114. The first beam collimator 602may be configured to receive light from the optical fiber 112, collimatethe light into a beam, and direct the beam toward the etalon 604.

FIG. 6B illustrates an etalon operating at a Brewster-angle in FIG. 6A.The etalon 604 is positioned at a ‘Brewster angle’ with respect to thecollimated light from collimator 602 to reduce or eliminate reflectionfrom the front surface of the etalon 604. The second beam collimator 606may be configured to collect the beam that was transmitted through theetalon 604 and direct it into the optical fiber 114.

FIG. 7A illustrates an example etalon filter 700, arranged in accordancewith at least some embodiments described in this disclosure. The etalonfilter 700 may be employed as the etalon filter 220 in the system 200 ofFIG. 2.

The etalon filter 700 may include a beam collimator 702 and an etalon704. The beam collimator 702 may be connected to the optical fiber 112.The beam collimator 702 may be configured to receive light from theoptical fiber 112, collimate the light into a beam, and direct the beamtoward the etalon 704.

FIG. 7B illustrates an etalon operating at a Brewster-angle in FIG. 7A.The etalon 704 is positioned at a ‘Brewster angle’ with respect to thecollimated light from collimator 702 to reduce or eliminate anyreflection from the front surface of the etalon 704. The beam collimator702 may also be configured to collect the beam that was reflected fromthe etalon 704 and direct it into the optical fiber 112.

FIG. 8 illustrates a simulated spectrum 800 that may be obtained usingany of the example systems of FIGS. 1-4. In particular, the spectrum 800may be obtained by the spectrometer 122 of any of the systems of FIGS.1-4 after the light has been reflected from or transmitted through theslab of material 102, where the slab of material is a 2000 um thicksapphire plate acting as a wafer carrier, and the etalon-filter is a2050 um thick Si etalon.

FIG. 9A illustrates a simulated spectrum 900 that may be measured by aspectrometer of any of the example systems of FIGS. 1-4, FIG. 9Billustrates a simulated spectrum 910 that may be reflected from a slabof material, and FIG. 9C illustrates a simulated normalized spectrum 920that may result from dividing the simulated spectrum 910 using thesimulated spectrum 900. In particular, the simulated spectrum 900 is ofa linearly polarized light source having a bandwidth half width halfmaximum 25 nm and centered at 1250 nm, as measured by a spectrometerhaving a bandwidth of 0.2 nm. The simulated spectrum 910 is reflectedfrom a slab of material having a thickness of 0.6 mm, a refractive indexof 3.5, and a reflection coefficient of each surface of 0.5, afterhaving passed through an etalon filter having a thickness of 0.74 mm, arefractive index of 3.5, and a reflection coefficient of each surface of0.5.

FIG. 10 is a flowchart of an example method 1000 for inspecting a slabof material, arranged in accordance with at least some embodimentsdescribed in this disclosure. The method 1000 may be implemented, insome embodiments, by a system, such as any of the systems 100, 200, 300,and 400 of FIGS. 1, 2, 3, and 4, respectively. Although illustrated asdiscrete blocks, various blocks may be divided into additional blocks,combined into fewer blocks, or eliminated, depending on the desiredimplementation.

In some embodiments, block 1002 may include emitting, from a broadbandlight source, light over single mode optical fiber. Additionally oralternatively, block 1002 may include emitting, from a linearlypolarized broadband light source, light over a polarization maintainingsingle mode optical-fiber. The plane of polarization or a direction ofpolarization of light from the linearly-polarized source may bepre-defined.

Block 1004 may include receiving, at a beam-forming assembly, the lightover the optical fiber and directing, at the beam-forming assembly, thelight toward a slab of material. In some embodiments, the block 1004 mayfurther include splitting, at the beam-forming assembly, the light intofirst and second portions after receiving, at the beam-forming assembly,the light over the optical fiber, directing, at the beam-formingassembly, the first portion of the light toward the slab of material,directing, at the beam-forming assembly, the second portion of the lightonto a reflector, combining, at the beam-forming assembly, the firstportion of the light after being reflected from the slab of material andthe second portion of the light after being reflected from thereflector, and directing, at the beam-forming assembly, the combinedlight over the optical fiber.

In some embodiments, block 1004 may include controlling, by a half-waveplate or any other polarization-rotator, polarization of the lightdirected to the slab of material from the beam-assembly. Morespecifically, the half-wave plate controls the plane of polarization ofthe light directed to the slab of material by rotating the plane ofpolarization through a pre-defined angle.

Block 1006 may include receiving, at a computer-controlled etalonfilter, the light over the optical fiber either before the light isdirected toward the slab of material or after the light has beenreflected from or transmitted through the slab of material. The etalonwithin the etalon filter may be placed at a Brewster-angle with respectto the incoming or incident light to reduce reflection from afront-surface thereof.

Block 1008 may include filtering the light at the etalon-filter.

Block 1010 may include directing, at the etalon filter, the light overthe optical fiber.

Block 1012 may include receiving, at a computer-controlled spectrometer,the light over the optical fiber after the light has been filtered bythe etalon-filter and after the light has been reflected from ortransmitted through the slab of material. The computer-controlledspectrometer may include the dispersive element as a grating, which maybe positioned to facilitate a pre-determined angle between at least onegroove thereof and the plane of polarization of the light received overthe optical-fiber. Additionally or alternatively, thecomputer-controlled spectrometer may include the dispersive element as aprism, wherein the prism is positioned at a Brewster-angle with respectto an incident light (e.g., the polarized light) to reduce reflectionfrom a first-surface thereof.

Block 1014 may include spectrally analyzing the light at thespectrometer. In some embodiments, the block 1014 may includedetermining a topography of one or more surfaces of the slab of materialand/or determining a thickness of the slab of material. In an example,the spectrometer may be provided with etalon for the purposes ofrendering interference that is captured as a part of spectral-analysis.

One skilled in the art will appreciate that, for this and other methodsdisclosed in this disclosure, the functions performed in the methods maybe implemented in differing order. Furthermore, the outlined operationsare only provided as examples, and some of the operations may beoptional, combined into fewer operations, or expanded into additionaloperations without detracting from the essence of the disclosedembodiments.

For example, in some embodiments, blocks 1008, 1010, and 1012 may beperformed prior to the block 1004, such as when the method 1000 isperformed by the system 300 of FIG. 3.

Further, in some embodiments, the method 1000 may further includereceiving, at a directional element, the light from the broadband lightsource over the optical fiber and directing, at the directional element,the light to the beam-forming assembly over the optical fiber,receiving, at the beam-forming assembly, the light reflected from theslab of material and directing, at the beam-forming assembly, the lightback to the directional element over the optical fiber, where the lightreceived at the etalon filter is received from the directional elementafter the light has been reflected from the slab of material and wherethe light received at the spectrometer is received from the etalonfilter, such as when the method 1000 is performed by the system 100 ofFIG. 1.

Further, in some embodiments, the method 1000 may further includereceiving, at a directional element, the polarized light from thelinearly polarized broadband light source over the polarizationmaintaining optical fiber and directing, at the directional element, thelight to the beam-forming assembly over the optical fiber, controlling,by the half wave plate or any other polarization rotator, thepolarization of light impinging the slab of material, receiving, at thebeam-forming assembly, the light reflected from the slab of material anddirecting, at the beam-forming assembly, the light back to thedirectional element over the optical fiber, where the light received atthe etalon filter is received from the directional element after thelight has been reflected from the slab of material and where the lightreceived at the spectrometer is received from the etalon filter, such aswhen the method 1000 is performed by the system 100 of FIG. 1.

Alternatively, in some embodiments, the method 1000 may further includereceiving, at a first directional element, the light from the broadbandlight source over the optical fiber and directing, at the firstdirectional element, the light to the beam-forming assembly over theoptical fiber, receiving, at the beam-forming assembly, the lightreflected from the slab of material and directing, at the beam-formingassembly, the light back to the first directional element over theoptical fiber, and receiving, at a second directional element, the lightfrom the first directional element over the optical fiber and directing,at the second directional element, the light to the etalon filter overthe optical fiber, where the light received at the etalon filter isreceived from the second directional element after the light has beenreflected from the slab of material. In these embodiments, the method1000 may further include directing, at the etalon filter, the light backto the second directional element over the optical fiber, where thelight received at the spectrometer is received from the seconddirectional element, such as when the method 1000 is performed by thesystem 200 of FIG. 2.

Alternatively, in some embodiments, the method 1000 may further includereceiving, at a first directional element, the light from the linearlypolarized broadband light source over the polarization maintainingoptical fiber and directing, at the first directional element, the lightto the beam-forming assembly over the optical fiber, controlling, by thehalf wave plate or any other polarization rotator, the polarization oflight impinging the slab of material, receiving, at the beam-formingassembly, the light reflected from the slab of material and directing,at the beam-forming assembly, the light back to the first directionalelement over the optical fiber, and receiving, at a second directionalelement, the light from the first directional element over the opticalfiber and directing, at the second directional element, the light to theetalon filter over the optical fiber, where the light received at theetalon filter is received from the second directional element after thelight has been reflected from the slab of material. In theseembodiments, the method 1000 may further include directing, at theetalon filter, the light back to the second directional element over theoptical fiber, where the light received at the spectrometer is receivedfrom the second directional element, such as when the method 1000 isperformed by the system 200 of FIG. 2.

Alternatively, in some embodiments, the method 1000 may further includereceiving, at a directional element, the light from the etalon filterover the optical fiber and directing, at the directional element, thelight to the beam-forming assembly over the optical fiber, where thelight received at the etalon filter is received from the broadband lightsource before the light is directed toward the slab of material. Inthese embodiments, the method 1000 may further include receiving, at thebeam-forming assembly, the light reflected from the slab of material anddirecting, at the beam-forming assembly, the light back to thedirectional element over the optical fiber, where the light received atthe spectrometer is received from the directional element, such as whenthe method 1000 is performed by the system 300 of FIG. 3.

In these or other embodiments, the method 1000 may further includereceiving, at a directional element, the light from the etalon filterover the optical fiber and directing, at the directional element, thelight to the beam-forming assembly over the optical fiber, where thelight received at the etalon filter is received from the linearlypolarized broadband light source before the light is directed toward theslab of material. In these embodiments, the method 1000 may furtherinclude controlling, by the half wave plate or any other polarizationrotator, the polarization of light impinging the slab of material,receiving, at the beam-forming assembly, the light reflected from theslab of material and directing, at the beam-forming assembly, the lightback to the directional element over the optical fiber, where the lightreceived at the spectrometer is received from the directional element,such as when the method 1000 is performed by the system 300 of FIG. 3.

Alternatively, in some embodiments, the method 1000 may further includereceiving, at a second beam-forming assembly, the light transmittedthrough the slab of material and directing, at the second beam-formingassembly, the light to the etalon filter over the optical fiber, wherethe light received at the etalon filter is received from the secondbeam-forming assembly after the light has been transmitted through theslab of material, and where the light received at the spectrometer isreceived from the etalon filter, such as when the method 1000 isperformed by the system 400 of FIG. 4.

Terms used in this disclosure and especially in the appended claims(e.g., bodies of the appended claims) are generally intended as “open”terms (e.g., the term “including” should be interpreted as “including,but not limited to,” the term “having” should be interpreted as “havingat least,” the term “includes” should be interpreted as “includes, butis not limited to,” etc.).

Additionally, if a specific number of an introduced claim recitation isintended, such an intent will be explicitly recited in the claim, and inthe absence of such recitation no such intent is present. For example,as an aid to understanding, the following appended claims may containusage of the introductory phrases “at least one” and “one or more” tointroduce claim recitations. However, the use of such phrases should notbe construed to imply that the introduction of a claim recitation by theindefinite articles “a” or “an” limits any particular claim containingsuch introduced claim recitation to embodiments containing only one suchrecitation, even when the same claim includes the introductory phrases“one or more” or “at least one” and indefinite articles such as “a” or“an” (e.g., “a” and/or “an” should be interpreted to mean “at least one”or “one or more”); the same holds true for the use of definite articlesused to introduce claim recitations.

In addition, even if a specific number of an introduced claim recitationis explicitly recited, those skilled in the art will recognize that suchrecitation should be interpreted to mean at least the recited number(e.g., the bare recitation of “two recitations,” without othermodifiers, means at least two recitations, or two or more recitations).Furthermore, in those instances where a convention analogous to “atleast one of A, B, and C, etc.” or “one or more of A, B, and C, etc.” isused, in general such a construction is intended to include A alone, Balone, C alone, A and B together, A and C together, B and C together, orA, B, and C together, etc. For example, the use of the term “and/or” isintended to be construed in this manner.

Further, any disjunctive word or phrase presenting two or morealternative terms, whether in the description of embodiments, claims, ordrawings, should be understood to contemplate the possibilities ofincluding one of the terms, either of the terms, or both terms. Forexample, the phrase “A or B” should be understood to include thepossibilities of “A” or “B” or “A and B.”

All examples and conditional language recited in this disclosure areintended for pedagogical objects to aid the reader in understanding theinvention and the concepts contributed by the inventor to furthering theart, and are to be construed as being without limitation to suchspecifically recited examples and conditions. Although embodiments ofthe present disclosure have been described in detail, it should beunderstood that various changes, substitutions, and alterations could bemade hereto without departing from the spirit and scope of the presentdisclosure.

1. A system for inspecting a slab of material, the system comprising:single mode optical fiber; a broadband light source configured to emitlight with wavelengths in a range from 780 nanometers (nm) to 1800 nmover the optical fiber; a beam-forming assembly configured to receivethe light over the optical fiber and direct the light toward a slab ofmaterial; a computer-controlled etalon filter configured to receive thelight over the optical fiber either before the light is directed towardthe slab of material or after the light has been reflected from ortransmitted through the slab of material, filter the light, and directthe light over the optical fiber; and a computer-controlled spectrometerconfigured to receive the light over the optical fiber after the lighthas been filtered by the etalon filter and after the light has beenreflected from or transmitted through the slab of material andspectrally analyze the light.
 2. The system of claim 1, wherein thebroadband light source is configured to emit light with wavelengths in arange of 780 nm to 1000 nm.
 3. The system of claim 1, wherein thebroadband light source is configured to emit light with wavelengths in arange of 800 nm to 1000 nm.
 4. The system of claim 3, wherein thecomputer-controlled spectrometer comprises a silicon-based detector. 5.The system of claim 1, wherein the broadband light source is configuredto emit light with wavelengths in a range of 1100 nm to 1800 nm.
 6. Thesystem of claim 1, wherein the broadband light source is configured toemit light with wavelengths in a range of 1200 nm to 1500 nm.
 6. Thesystem of claim 6, wherein the computer-controlled spectrometercomprises an Indium Gallium Arsenide detector.
 7. The system of claim 1,wherein the broadband light source comprises a Superluminescent LightEmitter Device.
 8. The system of claim 1, wherein each of the singlemode fiber, the beam-forming assembly, the computer-controlled etalonfilter, and the computer-controlled spectrometer are configured tooperate in the same wavelength range as the light emitted by thebroadband light source.
 9. A system for inspecting a slab of material,the system comprising: single mode optical fiber; a broadband lightsource configured to emit light over the optical fiber; a beam-formingassembly configured to: receive the light over the optical fiber; splitthe light, at a beam splitter, into first and second portions afterreceiving the light over the optical fiber; direct the first portion ofthe light toward the slab of material; direct the second portion of thelight onto a reflector that is maintained at a substantially constantdistance from the beam splitter; combine the first portion of the lightafter being reflected from the slab of material and the second portionof the light after being reflected from the reflector; and direct thecombined light over the optical fiber; a computer-controlled etalonfilter configured to receive the light over the optical fiber eitherbefore the light is directed toward the slab of material or after thelight has been reflected from or transmitted through the slab ofmaterial, filter the light, and direct the light over the optical fiber;and a computer-controlled spectrometer configured to receive the lightover the optical fiber after the light has been filtered by the etalonfilter and after the light has been reflected from or transmittedthrough the slab of material and spectrally analyze the light.
 10. Thesystem of claim 9, wherein the beam-forming assembly is comprised ofmaterials having a low coefficient of thermal expansion such that inresponse to an increase or decrease in a temperature of the system, thereflector is maintained at a substantially constant distance from thebeam splitter.
 11. The system of claim 10, wherein the beam-formingassembly is comprised of Invar.
 12. The system of claim 9, furthercomprising a temperature controller that is configured to maintain thebeam-forming assembly at a substantially constant temperature.
 13. Thesystem of claim 12, wherein the temperature controller comprises atemperature sensor, a heater, and feedback electronics.
 14. The systemof claim 12, wherein the temperature controller comprises athermoelectric cooler.